The young Prince William made the same trip when he accompanied his parents on their six-week tour of Australasia in 1983, staying with his nanny on a ranch in the outback where his parents visited him as often as they could.

The Duke and Duchess visited Canada for their first joint foreign tour in 2011, then visited the Far East last year. Because Australia and New Zealand, together with Canada, make up the largest of the Commonwealth realms, the couple seem certain to put them next on their itinerary.

The choice of Australia for the new baby’s first official trip abroad would not only make up for the fact that the country has had to wait so long to see the Duchess, but would also have the benefit of shoring up support for the monarchy in a country where republicanism is never far from the political agenda.

Before then, the Duke and Duchess have a more pressing matter to attend to, that of registering their son’s birth.

They have 42 days to register the prince’s birth at Westminster Register Office, though the registrar will travel to Kensington Palace to complete the formalities before a birth certificate is issued. The next date in the baby’s diary will be its christening, which is likely to happen after the Royal family’s annual summer break at Balmoral, making a date in September or October likely.

The christening is likely to take place in the Music Room at Buckingham Palace, where Prince William and previous generations of the Royal family have been baptised.

The Archbishop of Canterbury is expected to officiate at the ceremony, and the baby prince will wear a christening robe of Honiton lace lined with satin, which is a replica of a robe made in 1841 for Queen Victoria’s eldest daughter, and which was used for more than 30 royal christenings up to and including Prince William. The replica was made in 2008 by the Queen’s dressmaker, Angela Kelly, because the original had become too fragile.

The Duchess and the Duke, who has two weeks’ statutory paternity leave from the RAF, are expected to spend some time at their London residence in Kensington Palace before then, but will probably spend most of their time with the Duchess’s parents in Bucklebury, Berks.

The Queen leaves for Balmoral on Friday and the Prince of Wales has a busy programme for the rest of July, meaning that the Duke and Duchess will turn to the Middletons for company and support as they learn the ropes of parenthood.

The Queen has extended an invitation for the Duchess and the Middletons to stay at Balmoral, and it remains a possibility that they may spend some time there in the coming weeks.

The Duke and Duchess will also have to turn their thoughts to their son’s schooling. The Duke is likely to favour putting his son’s name down for Eton, where he and his brother, Prince Harry, were educated, but the baby’s primary school will be dictated by the Duke’s next career move.

With his tour of duty at RAF Valley in Wales finishing in September, the Duke has already decided what he will do next, though he has not made it public knowledge.

He will either stay in the RAF but move to another base, transfer to another branch of the Armed Forces, or end his military career to take up full-time royal duties.

The location of the couple’s new home when they leave their rented farmhouse on Anglesey, which will depend upon the Duke’s next choice of career, will determine which primary school the prince attends.

If the Duke opts for a London-based military posting or full-time royal duties, he might want to send his son to his primary school, Wetherby pre-preparatory in Notting Hill, where the fees are £5,490 per term.

The Duchess went to St Andrew’s prep school in Pangbourne, Berkshire, a few miles from her family home, before boarding at Marlborough College in Wiltshire.